In flat spacetime one can also define twistors via solutions to the twistor equation (see [1]}),
but in general curved spacetimes this equation has no solutions so the definition via (REF )
is slightly more general, see [2]}, [3]}, [4]}.
The existence of twistor surfaces is however still quite restrictive;
in particular, the usual twistor space of twistor theory is 3-dimensional and it requires
the Weyl curvature to be (anti-)self-dual.
